What function do you know from calculus is such that its first derivative is itself? its first derivative is a constant multiple of itself? write each answer in the form of a first-order differential equation with a solution.

First Part:

exponential function is the one whose first order derivative is the function itself.

Second Part:

Third Part:

Step-by-step explanation:

First Part:

In calculus exponential function is the one whose first order derivative is the function itself.

Where:

t is independent variable.

Derivative is represented as:

Where:

c is any number.

Second Part:

Consider the constant A.

The function will become:

Third Part:

Derivative is represented as:

Where:

c is any number.

ddsf

step-by-step explanation:

dfs

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.